
The conditions of the theorem are not strong enough to guarantee that \(L^{\prime }\)  is strongly finitary and thus has a presentation by operations and equations. As shown in [1]}, this is the case if \(T\)  preserves weak pullbacks.

In the case of graded modal logic, \(L\)  is different from \(\mathsf {P}T\mathsf {S}\)  even on finite \(\mathbf {BA}\) s. Therefore, the approach of [1]} cannot be applied. We leave a description of the positivication of graded modal logic for a sequel.


